The Sun says Dubai Investment Capital are still hopeful of taking control of the club and have targeted George Gillett's 50 per cent holding in the Reds.
But despite Benitez getting a vote of confidence from Liverpool's American owners recently, DIC are unhappy at the side's performances this term.
They are 19 points off leaders Arsenal and face a fight to even haul themselves into a Champions League finishing slot.
That has piled the pressure back on the Spaniard ahead of Tuesday's last-16 first-leg showdown with Serie A pacesetters Inter.
Defeat would prove a hammer blow to the stretched finances of the club, putting Benitez back on the brink.